A CITB insider said the issue was raised at a board meeting last week after a number of local authorities asked the training body to improve their performance.
The insider said: "We are drawing up a working plan to take to the government so that we can implement the taking over of training of local authority direct labour organisations."
He added that a similar plan of action was being considered for taking over the training of rail contractors now that the CITB had become a sector skills council.
The insider said the CITB's board was waiting for the appropriate time to approach Network Rail chief executive John Armitt with the plan.
He said: "There is still some confusion as to what is happening with rail maintenance contractors and whether they are being brought in house at Network Rail or not. Once this and the implications of any decision have been concluded, we will put our case."
Building revealed last month that the CITB was in talks to introduce a shake up in rail safety training.